Lemma 2.3  [1]}

If \(\Omega \)  is a simply connected open subset of \(\mathbb {R}^2\)  and \(A \in \mathcal {B} (\Omega ,\operatorname{Sym})\)  then
\(\operatorname{Curl}\operatorname{Curl}A=0\) 
is equivalent to the existence of a vector field \(U \in \mathcal {B} (\Omega , \mathbb {R}^2)\) , with \(U(\phi )=\int _\Omega \langle u,\phi \rangle \operatorname{da}\)  for any \(\phi \in \mathcal {D}(\Omega -O,\mathbb {R}^2)\) , where \(u\)  is a piecewise smooth vector field continuous across \(S\) , such that
\(A= (1/2)\left({\nabla U +(\nabla U)^T}\right)\) .

